Hybrid Quantum-Classical Eigensolver Without Variation or Parametric Gates
Abstract
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground sate and excited states of BeH and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H molecule.
Cite
@article{arxiv.2008.11347,
title = {Hybrid Quantum-Classical Eigensolver Without Variation or Parametric Gates},
author = {Pejman Jouzdani and Stefan Bringuier},
journal= {arXiv preprint arXiv:2008.11347},
year = {2023}
}